13,19 8. Find the length of the curve r(t) = (21-0≤t≤1.9. The helix r₁(t)= cos ti+ sin tj + tk intersects the curver₂(t) = (1 + t)i + t2j+t³k at the point (1, 0, 0). Find theangle of intersection of these curves.siga10. Reparametrize the curve r(t) = e'i + e' sin tj + e' cost kwith respect to arc length measured from the point (1, 0, 1)in the direction of increasing t.11. For the curve given by r(t) = (sin³t, cos³t, sin²t),0 ≤t≤ π/2, find365 X 21(a) the unit tangent vector,(b) the unit normal vector, (1 1010(c) the unit binormal vector, andpont (d) the curvature. libyluonnonSTUIN 5112. Find the curvature of the ellipse x = 3 cos t, y = 4 sin tatthe points (3, 0) and (0, 4).13. Find the curvature of the curve y = x4 at the point (1, 1).14. Find an equation of the osculating circle of the curvey = x - x² at the origin. Graph both the curve and itsosculating circle.i.tlls to15. Find an equation of the osculating plane of the curvex = sin 2t, y = t, z = cos 2t at the point (0, 7, 1). 8. Find the length of the curve r(t) = (21-0≤t≤1.9. The helix r₁(t)= cos ti+ sin tj + tk intersects the curver₂(t) = (1 + t)i + t2j+t³k at the point (1, 0, 0). Find theangle of intersection of these curves.siga10. Reparametrize the curve r(t) = e'i + e' sin tj + e' cost kwith respect to arc length measured from the point (1, 0, 1)in the direction of increasing t.11. For the curve given by r(t) = (sin³t, cos³t, sin²t),0 ≤t≤ π/2, find365 X 21(a) the unit tangent vector,(b) the unit normal vector, (1 1010(c) the unit binormal vector, andpont (d) the curvature. libyluonnonSTUIN 5112. Find the curvature of the ellipse x = 3 cos t, y = 4 sin tatthe points (3, 0) and (0, 4).13. Find the curvature of the curve y = x4 at the point (1, 1).14. Find an equation of the osculating circle of the curvey = x - x² at the origin. Graph both the curve and itsosculating circle.i.tlls to15. Find an equation of the osculating plane of the curvex = sin 2t, y = t, z = cos 2t at the point (0, 7, 1).

13. Answer To find the curvature of the curve y = x^4 at the point (1,1), we need to find the radius…

13. Find the curvature of the curve y = x at the point (1, 1). 14. Find an equation of the osculating circle of the curve y = x - x² at the origin. Graph both the curve and its osculating circle. 15. Find an equation of the osculating plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, 7, 1).

13. Find the curvature of the curve y = x at the point (1, 1). 14. Find an equation of the osculating circle of the curve y = x - x² at the origin. Graph both the curve and its osculating circle. 15. Find an equation of the osculating plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, 7, 1).

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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